Device and method for detecting the rotational movement of an element rotatably mounted about an axis

ABSTRACT

A device for detecting the rotational movement of an element which is rotatably seated around an axis, the device including a material measure that rotates about an axis of rotation. A first measuring graduation provided on the material measure and which scans along a first direction, which has a component along the axis of rotation and a second measuring graduation provided on the material measure, wherein both the first measuring graduation and the second measuring graduation surround the axis of rotation in a ring shape, and which can be scanned along the first direction and a second direction that is linearly independent of the first direction. At least three measuring heads, which are spaced apart from each other along a circumferential direction which surrounds the axis of rotation, are assigned to each of the first measuring graduation and the second measuring graduation for scanning the first measuring graduation and the second measuring graduations.

Applicant claims, under 35 U.S.C. § 120 and 365, the benefit of priorityof the filing date of May 31, 2001 of a Patent Cooperation Treaty patentapplication, copy attached, Ser. No. PCT/DE01/02107, filed on theaforementioned date, the entire contents of which are incorporatedherein by reference, wherein Patent Cooperation Treaty patentapplication Ser. No. PCT/DE01/02107 was not published under PCT Article21(2) in English.

Applicant claims, under 35 U.S.C. § 119, the benefit of priority of thefiling date of Sep. 18, 2000 of a German patent application, copyattached, Ser. No. 100 47 776.3, filed on the aforementioned date, theentire contents of which are incorporated herein by reference.

BACKGROUND OF THE INVENTION

1. Field of the Invention

The present invention relates to a device and a method for detecting therotational movement of an element which is rotatably seated around anaxis, in particular a turntable.

2. Discussion of Related Art

The detection of the rotational movement takes place for the purpose ofdetermining deviations from an ideal rotational movement around apredetermined axis. For example, this can be a so-called calibratingmeasurement, wherein the detected deviations of a rotational movementfrom an ideal rotational movement can be used for a subsequentcalibration. This means that the knowledge of the deviations from anideal rotation which have occurred can be taken into consideration bycalculation in the course of a subsequent use of the rotationally seatedelement, for example a turntable or a machine tool spindle.

The deviations of the rotational movement of a turntable or otherrotationally seated element from an ideal rotational movement around apredetermined axis can be separated into six individual deviations,namely respectively three translatory and rotary deviations.

A method and a device for measuring turntable deviations are known fromDE 36 37 410 C2, wherein the turntable is arranged within the measuringvolume of a coordinate measuring device, and the deviations are detectedwith the aid of the coordinate measuring device in that a test member isfastened on the turntable, which has a multitude of measuring pointsformed by contact faces, and that respective sets of measuring pointcoordinates are measured by the coordinate measuring device by means ofcontact in various angular positions of the turntable. The turntabledeviations are calculated by means of these sets of measuring points.This method has the disadvantage that contact with the test member isrequired and that the individual deviations can only be determined in asequence of several measurements.

A method for measuring the deviation of rotating axes by means of testspheres or test cylinders is described in the reference“Werkzeugmaschinen und Fertigungssysteme” [Machine Tools and ProductionSystems], vol. 4, VDI publishers, 1996, p. 149 et seq. The methodsmentioned there have the disadvantage, however, that each only permitsthe measuring of a portion of the six individual deviations.

SUMMARY AND OBJECTS OF THE INVENTION

An object of the present invention is based on providing a device and amethod for detecting the rotational movement of an element which isrotatably seated around an axis, which make possible the completedetermination of the occurring individual deviations, or a compensationof the individual deviations during a measurement.

In accordance with the present invention, this object is attained bycreating a device for detecting the rotational movement of an elementwhich is rotatably seated around an axis, the device including amaterial measure that rotates about an axis of rotation. A firstmeasuring graduation provided on the material measure and which scansalong a first direction, which has a component along the axis ofrotation and a second measuring graduation provided on the materialmeasure, wherein both the first measuring graduation and the secondmeasuring graduation surround the axis of rotation in a ring shape, andwhich can be scanned along the first direction and a second directionthat is linearly independent of the first direction. At least threemeasuring heads, which are spaced apart from each other along acircumferential direction which surrounds the axis of rotation, areassigned to each of the first measuring graduation and the secondmeasuring graduation for scanning the first measuring graduation and thesecond measuring graduations.

This object is also attained by a method for detecting rotationalmovement of an element which rotates around an axis of rotation, themethod including arranging a first measuring graduation that surroundsan axis of rotation around which an element rotates and arranging asecond measuring graduation that surrounds the axis of rotation.Scanning the first measuring graduation along a first direction having acomponent along the axis of rotation, wherein the scanning the firstmeasuring graduation takes place in at least three locations, which arespaced apart from each other in a circumferential direction surroundingthe axis of rotation. Scanning the second measuring graduation along asecond direction that is linearly independent of the first direction,wherein the scanning the second measuring graduation takes place in atleast three locations, which are spaced apart from each other in thecircumferential direction surrounding the axis of rotation.

The device in accordance with the invention includes a material measurearranged coaxially with respect to the element to be measured, forexample a turntable, and two measuring graduations provided on thematerial measure, which surround the axis of rotation of the materialmeasure in a ring shape and which are embodied for scanning twodirections which are linearly independent of each other. In this case atleast one measuring graduation is intended for scanning along adirection which has a component along the axis of rotation, and at leastthree measuring heads, which are spaced apart from each other along thecircumference of the material measure, are assigned to each materialmeasure for scanning the respective measuring graduation.

The material measure can be a test member which can be connected withthe element to be measured. However, the material measure can also beintegrated into the element to be measured (for example a turntable).

By scanning one of the measuring graduations by means of three measuringheads, which are spaced apart from each other along the circumference ofthe material measure, it is possible to determine the linearlyindependent individual deviations of the axis of rotation with respectto the predetermined ideal axis. Since the two measuring graduations arealso being scanned along two directions which are linearly independentof each other (i.e., they cannot be transferred into each other by alinear linkage), it is possible in this way to determine six individualdeviations, i.e. to detect all individual deviations with respect to anideal rotational movement around a predetermined axis.

The determination of the individual deviations from the values which canbe measured by means of the device of the invention are explained indetail further down by means of FIGS. 7 and 8.

The attainment of the object in accordance with the invention has theadvantage that the determination of all six individual deviations can beperformed simultaneously, position-dependent and continuously with ameasuring arrangement by a contactless-operating, high-resolution andhighly accurate measuring method. By this a complete compensation of alldeviations from an ideal rotational movement is made possible with asingle measurement in that the individual deviations are taken intoconsideration by calculation in the course of later applications.

The device in accordance with the invention can be used, inter alia, foracceptance tests and the calibration of turntables on the basis of astatic or dynamic measurements of the turntable, for the determinationof positioning and reversal errors, for performing step-response testsand for determining thermal drift.

Moreover, in the course of employment in regulated operations an ONLINEcompensation of eccentricity deviations is made possible. In particular,in accordance with a further development of the invention it can beprovided that a correction of the measured values, which are detectedduring the operation of the turntable or any other rotatable element fordetermining its position, in particular angles of rotation, is madeimmediately (ONLINE correction).

In a preferred embodiment of the invention, the two measuringgraduations can be scanned vertically with respect to each other. If thetwo measuring graduations are formed by line graduations, this can beperformed in a simple manner in that the lines of one measuringgraduation extend vertically with respect to the lines of the othermeasuring graduation. For example, one measuring graduation can bescanned in the axial direction, i.e. parallel with the axis of rotation,and the other measuring graduation can be scanned in a tangentialdirection with respect to the axis of rotation.

The measuring graduations can in particular be constituted byincremental measuring graduations; however, the use of measuringgraduations providing an absolute position information is also easilypossible.

In a particularly preferred embodiment of the invention, the twomeasuring graduations are formed by a cross grating graduation extendingon a surface of the material measure, in particular of a cylindricalmaterial measure, along its circumference. The cross grating graduationcan be formed by two line graduations extending vertically with respectto each other, as well as by a chessboard graduation.

On the other hand, the two measuring graduations can also be arrangedspatially separated, for example one measuring graduation on a surfaceof the material measure, and the other measuring graduation on acircular ring projecting outward away from the surface.

The resulting measuring direction from the two measuring directionsalong which the measuring graduations are scanned preferably forms,together with the axis of rotation, a pair of straight lines, which areskewed with respect to each other, at each measuring point, i.e. thestraight line on which the resulting measuring direction is locatedextends neither parallel to the axis of rotation nor intersects it.

It is possible by means of an additional reference marker track tocompensate the so-called long-wave graduation error by using acorrection table. Further than that it is possible to use the referencepulse for triggering the measurement.

When using a cylindrical material measure, its diameter (vertically withrespect to the axis of rotation) should be selected to be as large aspossible in order to be able to detect individual deviations by means ofthe greatest possible resolution.

In accordance with a variant of the invention, three measuring heads areprovided for scanning the two measuring graduations, each of which scanstwo measuring graduations. In this case therefore the same measuringheads are used for scanning both measuring graduations. This variant ofthe invention can be advantageously employed in particular in thosecases in which the two measuring graduations are constituted by a crossgraduation. In this case the three measuring heads are designed as crossgrating measuring heads, by means of which the cross grating graduationcan be scanned.

Preferably the three measuring heads are arranged at a distance ofrespectively 120°—in relation to the axis of rotation of the materialmeasure—along the circumference of the material measure.

In accordance with another variant of the invention, six measuring headsare provided for scanning the two measuring graduations, wherein threemeasuring heads are assigned to each measuring graduation. In this case,for example three measuring heads scan the one measuring graduation inthe axial direction, and three further measuring heads scan the othermeasuring graduation in the axial direction. For this purpose themeasuring heads provided for scanning the one and the other measuringgraduation are each arranged alternatingly one behind the other alongthe circumference of the material measure, preferably at an angulardistance of respectively 60°.

When employing six measuring heads in particular, in a furtherdevelopment of the invention these can be advantageously wired to eachother in such a way, that the position, in particular the actual angleof rotation, of the rotatable element can be determined by means of themeasured values from the individual measurable quantities produced fromthe output signals, by means of which an immediate correction (ONLINEcorrection) of the position, or the angular measured value affected bytolerances, is made possible in the course of performing a measurement.

For this purpose the measuring heads are wired together in such a waythat the measured values from the measuring heads intended for the(axial) scanning of the one measuring graduation are linked for formingsecond order terms, and that the measured values of the measuring headsintended for the (tangential) scanning of the other measuring graduationare linearly inserted into the determination of the angle of rotation.

Besides the three, or six, measuring heads required for scanning the twomeasuring graduations, at least one additional measuring head can beprovided for generating a redundant output signal. Thus, instead ofthree measuring heads at angular distances of 120° each, it is possible,for example, to arrange respectively four measuring heads at an angulardistance of 90° each along the circumference of the material measure.Because of this, there is the possibility of compensating higher ordererrors, for example second order eccentricity errors (ellipticalgraduation), or second order axial wobble (curved graduation).

Preferably all measuring heads are fastened on a common support in orderto be able to fix a defined relative arrangement, wherein the supportmust be fixed in place in a suitable manner, for example on a machinetool spindle in case of measuring a turntable.

The material of the holder must be selected in such a way that itsthermal expansion behavior corresponds to that of the support of themeasuring graduation. In this case a test member itself can be used asthe support of the measuring graduation, for example, or the measuringgraduation is provided on a separate measuring tape fastened on the testmember.

The method in accordance with the present invention for detecting therotational movement of an element rotatably seated around an axis isdistinguished by a method for detecting rotational movement of anelement which rotates around an axis of rotation, the method includingarranging a first measuring graduation that surrounds an axis ofrotation around which an element rotates and arranging a secondmeasuring graduation that surrounds the axis of rotation. Scanning thefirst measuring graduation along a first direction having a componentalong the axis of rotation, wherein the scanning the first measuringgraduation takes place in at least three locations, which are spacedapart from each other in a circumferential direction surrounding theaxis of rotation. Scanning the second measuring graduation along asecond direction that is linearly independent of the first direction,therein the scanning the second measuring graduation takes place in atleast three locations, which are spaced apart from each other in thecircumferential direction surrounding the axis of rotation.

In the course of executing the method of the invention, the materialmeasure is rotated, preferably by at least one revolution, around itsaxis of rotation in relation to the locations (measuring heads), wherethe scanning of the material measure is performed. In this connection itis unimportant whether the material measure or the means (measuringheads) provided for scanning the material measure are rotated forperforming this relative movement.

The method of the invention is suitable for determining individualdeviations of the rotatable elements within the framework of acalibration measurement in order to be able to compensate theseindividual deviations during subsequent measurements, as well as for adirect ONLINE compensation of the individual deviations of the rotatableelement.

Further features and advantages of the invention will become apparent inthe course of the subsequent description, making reference to thedrawings.

Shown are in:

BRIEF DESCRIPTION OF THE DRAWING

FIG. 1 schematically shows a perspective representation of a turntablearranged on a machine foundation,

FIG. 2 schematically shows a perspective representation of a firstembodiment of a test member provided with a cross grating graduation inaccordance with the present invention, which can be connected with theturntable in FIG. 1 for determining individual deviations of the axis ofrotation of the turntable,

FIG. 3 schematically shows a variation of the cylindrical test member inFIG. 2, having two separate measuring graduations,

FIG. 4 schematically shows a first embodiment of an arrangement forscanning the test member in FIG. 2 in accordance with the presentinvention;

FIG. 5 schematically shows a second embodiment of an arrangement forscanning the test member in FIG. 2 in accordance with the presentinvention;

FIGS. 6 a and 6 b show two plan views of a clamping system in accordancewith the present invention by which the test member can be fastened onthe turntable to be surveyed;

FIG. 7 shows a geometric representation of the actual movement of theturntable of FIG. 1 to be surveyed,

FIG. 8 shows a geometric representation of the desired movement of theturntable of FIG. 1 to be surveyed,

FIG. 9 shows an arrangement in accordance with FIG. 5, which is intendedin particular for an ONLINE correction of individual deviations in thecourse of performing a measurement in accordance with the presentinvention;

FIG. 10 schematically shows an embodiment wiring of the measuring headsin the arrangement in accordance with FIG. 9, which is suitable for anONLINE correction in accordance with the present invention;

FIG. 11, shows a geometric representation of the actual movement of theturntable of FIG. 1 to be surveyed, wherein it is intended to perform anONLINE correction by means of the arrangement in FIGS. 9 and 10 inaccordance with the present invention.

DESCRIPTION IF THE PREFERRED EMBODIMENT(S) OF THE INVENTION

A machine foundation M with a turntable R, which has a turntable axis A,and which can be rotated (for example for processing a workpiece), isschematically represented in FIG. 1.

The object of the present invention is the detection of a rotationalmovement around this axis A for determining deviations from an idealrotational movement around a predetermined desired axis. Thus, as aresult the individual deviations of the turntable axis A in regard to anideal axis are determined.

Of importance here is in particular the detection of systematic errors,which can be systematically taken into consideration in the course ofthe control of the turntable. In the course of this the detection of theindividual deviations can take place, on the one hand, within theframework of a calibration measurement in order to be able to take theminto account during subsequent measurements using the turntable or, onthe other hand, for the immediate ONLINE correction, or compensation, ofthe individual deviations in the course of performing a measurement.

The individual deviations are composed of three so-called translatorydeviations and three so-called rotary deviations.

A first translatory deviation e_(z) relates to the axial deviation alongthe axis A which, in the present example, coincides with the z-directionof the coordinate system represented in FIG. 1 (local coordinate system,or non-rotating coordinate system of the turntable).

Two further translatory deviations ex and ey relate to the translatorydeviation in two spatial directions extending perpendicularly withrespect to each other vertically to the axis A. In the present example,these two spatial directions correspond to the x-axis and y-axis of theCartesian coordinate system, wherein the axis A defines the z-axis. Thedeviations, identified by the two last mentioned individual deviationsex and ey from an ideal rotational movement around a predetermineddesired axis, describe the eccentricity (eccentric deviation) of theactual rotational movement.

Of the three rotary individual deviations, one (δ) relates to the rotarydeviation around the axis A (z-axis). This deviation (δ) is called apositioning deviation (angular error) around the local z-axis.

The other two rotary individual deviations α and β identify the rotarydeviation with respect to the x- or y-axis. Such deviations lead to atumbling movement.

The angle of rotation error (positioning deviation) is here determinedby reference to a guide value, in particular by reference to a shaft,which drives the turntable (and therefore also the test member connectedwith the turntable).

A material measure in the form of a test member of the type representedin FIG. 2 can be used for detecting the six deviations (movement errorsor a rotational movement) represented in FIG. 1 and explained above inone measurement.

This test member is a cylindrical test member 1, which is connected withthe turntable R in FIG. 1 for detecting the individual deviations insuch a way that the axis of rotation A (center axis) of the cylindricaltest member 1 and the turntable axis A coincide.

On its outer surface 10, the cylindrical test member 1 has a crossgrating graduation 13. The latter consists of a first incremental linegraduation 11 with a plurality of parallel graduating lines, whichextend in the circumferential direction U of the test member 1 and arearranged at a constant distance from each other. The graduation lines ofa second graduation 12 extend perpendicularly with respect to thegraduating lines of this first graduation 11. Each of the latter extendsparallel with the axis of rotation A of the test member 1 (i.e. in theaxial direction), and are also arranged at a constant distance from eachother, so that again an incremental measuring graduation results.

By scanning the cross grating graduation 13 by means of suitablemeasuring heads, it is possible to determine the six individualdeviations e_(x), e_(y), e_(z), α, β and δ in the course of a rotationalmovement around the axis of the turntable R represented in FIG. 1 in onesingle measurement, and this in a manner positionally dependent for eachposition occurring during the rotational movement. This will beexplained in greater detail in what follows by means of FIGS. 4 and 5.

A further exemplary embodiment of a cylindrical test member isrepresented in FIG. 3. In this case the cylindrical test member 1 hasonly one measuring graduation 11 on its outer surface 10, which consistsof a plurality of lines, which are arranged at a constant distance fromeach other and extend along the circumference U of the test member 1.

A second measuring graduation 17 is provided on a ring 15 extendingalong the circumference of the cylinder-shaped test member 1 andconstitutes a circular surface 16, which projects vertically away fromthe surface 10 of the test member 1. The measuring graduation 17provided on this surface 16 consists of a plurality of lines, spacedapart from each other along the circumference U of the test member 1,each of which extends in the radial direction in relation to the axis ofrotation A of the cylindrical test member 1.

To sum up, in the exemplary embodiment in FIG. 2, as well as in theexemplary embodiment in FIG. 3, the lines of the one measuringgraduation 11 extend in the circumferential direction and are spacedapart from each other in the axial direction. This measuring graduation11 can therefore be scanned in the axial direction a (parallel with theaxis of rotation).

The lines of the other measuring graduation 12 or 17 each extendvertically in relation to the lines of the first measuring graduation 11and are spaced apart from each other along the circumference U of thecylindrical test member 1. Thus, the other measuring graduation 12 or 17can be scanned in the tangential direction t.

However, in this connection it is not absolutely necessary that thelines of the first graduation 11 extend exactly along thecircumferential direction U, and the lines of the second graduation 12or 17 vertically with respect to the lines of the first graduation 11.Instead, an inclined course of the lines of the individual graduations11, 12, 17 is also conceivable. It is only crucial that the onegraduation can be scanned in the axial direction and the othergraduation in a direction vertically to the first. It is sufficient forthis that the lines of the first graduation 11 have a component alongthe circumference U of the cylindrical test member 1, and that the linesof the other measuring graduation 12 or 17 have a component verticallyin relation to the circumferential direction U.

The measuring direction resulting from the axial and the tangentialmeasuring directions a or t is located (at any arbitrary measuring pointat the circumference of the test member 1) on a straight line, which isoriented skewed with respect to the axis of rotation A. This means thatthe respective straight line extends neither parallel to the axis ofrotation, nor does it intersect the latter. The said straight line alsodoes not extend in a plane located vertically with respect to the axisof rotation A.

An arrangement for scanning the cylindrical test member 1 with a crossgrating 13 is represented in FIG. 4. This arrangement comprises threemeasuring heads 2 in the form of cross grating reading heads, which arespaced apart from each other along the circumference U of thecylindrical test member 1 at a constant angular distance of 120°. Oneach of their surfaces 20 facing the surface 10 of the cylindrical testmember 1, these measuring heads 2 have a cross grating, see FIG. 6 a inthis connection, in which the surface 20 which is facing the surface 10of the measuring heads 2 embodied as cross grating reading heads can beseen.

The cross grating 11 on the surface 10 of the cylindrical test member 1can be scanned by means of each one of these measuring heads 2 in thetangential direction t (see FIG. 2), as well as in the axial direction(parallel with the axis of rotation A). In this case the scanning takesplace at three locations, which are spaced apart along the circumferenceU of the cylindrical test member 1, where the three measuring heads 2have been placed.

In the exemplary embodiment of FIG. 5, an arrangement of six measuringheads 3, 4 is used for scanning the cylindrical test member 1, which isprovided with a cross grating 13 on its surface 10, of which threemeasuring heads 3 scan the cross grating 13 (see FIG. 2) in the axialdirection, and of which three further measuring heads 4 scan the crossgrating 13 in the tangential direction. The measuring heads 3, 4 arearranged along the circumference U of the cylindrical test member atregular angular distances of 60°, wherewith respectively axiallyscanning measuring heads 3 and tangentially scanning measuring heads 4are alternatingly arranged. Accordingly, the angles ψ₂ to ψ₆ have thevalues of 60°, 120°, 180°, 240° and 300°.

In both cases, i.e. with the arrangement in accordance with FIG. 4, aswell as with the arrangement in accordance with FIG. 5, it is possibleto obtain information, in particular regarding the individual deviationse_(z), α and β by means of a measuring graduation, which determine theaxial error and tumbling, and by scanning in the tangential direction,information in particular regarding the individual deviations e_(x),e_(y) and δ, which determine the eccentricity and the positioningdeviation (angular error).

In this case the arrangement in accordance with FIG. 5 is particularlysuited for scanning a test member of the type represented in FIG. 3,wherein the scanning faces of the measuring heads must face therespectively assigned measuring graduation.

In accordance with FIGS. 6 a and 6 b, the measuring heads 2 (or 3, 4)are fastened on a common support H, which assures a defined relativeposition of the measuring heads 2. The support H must be fixed in place,uncoupled from the axis of rotation A of the turntable, or of the testmember. For this purpose it can be fixed in place by means of aconventional clamping system S in relation to the spindle of a machinetool, for example, whose turntable is to be surveyed.

In this connection the positioning of the triangularly-shaped support Hand the three measuring heads 2 fastened thereon in relation to the testmember 1 and its outer surface 10 can be seen in a view from above inFIG. 6 b. In the lateral view in accordance with FIG. 6 a, however, thetest member 1 is not represented in order to make the individualmeasuring heads 2 and their surfaces 20 (scanning surfaces) facing thesurface 10 of the test member 1 better visible.

In what follows it will be explained by means of FIGS. 7 and 8 how thesix individual deviations of a turntable, obtained in the course ofperforming a measurement by the above described arrangements, from themeasured values for six measurable quantities, can be determined.

For performing a measurement with the aim of determining the six abovedefined independent deviations, the turntable is rotated by at least onerevolution with respect to the coordinate system of a fixed part of theappropriate machine tool, and therefore relative to the coordinatesystem of the measuring heads. In the ideal case, the rotation of theturntable is purely a rotational movement around a predetermined axis.However, because of production and assembly tolerances, the turntableperforms in fact an interfering movement, which is superimposed on thepurely rotational movement and is to be determined and compensated.

In accordance with FIGS. 7 and 8, the description of the generalrotational movement of the turntable requires two coordinate systems,wherein FIG. 7 relates to the actual movement and FIG. 8 to the desiredmovement of the turntable. In this case let the coordinate system I bethe spatially fixed system (coordinate system of the appropriate machinetool, or of the measuring heads), with respect to which the movement ofthe turntable is described, wherein its own coordinate system P isassigned to the latter, in which the geometry of the turntable isdefined.

The orthogonal transformation${\underset{\underset{\_}{\_}}{T}}_{i}^{PI},$exists between these two coordinate systems, which transforms thecoordinate system P into the coordinate system I. In this case thequantity w _(i) ^(I) of the actual movement results from the followingvector equation $\begin{matrix}{{\underset{\_}{w}}_{i}^{I} = {{\underset{\_}{e}}^{I} - {\underset{\_}{s}}^{I} + {{\underset{\underset{\_}{\_}}{T}}_{i}^{PI} \cdot {\underset{\_}{r}}^{P}}}} & (1)\end{matrix}$wherein

-   e ^(I) Eccentricity of the material measure-   s ^(I) Coordinates of the sensor head (measuring head)-   r ^(P) Radius vector of the material measure    ${\underset{\underset{\_}{\_}}{T}}_{i}^{PI},$-    Rotation matrix-   w _(i) ^(I) Measured value of the actual movement.

The rotation matrix ${\underset{\underset{\_}{\_}}{T}}_{i}^{PI}$contains three rotation parameters α, β and γ, which describe thegeneral rotation of the turntable in relation to the machine coordinatesystem. The angle of rotation γ is composed of the actual measurablequantity (measurement angle) φ and the orientation error δ(γ=φ+δ). Ifinitially only very small rotations as a whole are observed, thelinearized rotation matrix ${\underset{\underset{\_}{\_}}{T}}_{i}^{PI}$is obtained $\begin{matrix}{{\underset{\underset{\_}{\_}}{T}}_{i}^{PI} = \begin{bmatrix}1 & {- \left( {\varphi + \delta} \right)} & \beta \\{\varphi + \delta} & 1 & {- \alpha} \\{- \beta} & \alpha & 1\end{bmatrix}} & (2)\end{matrix}$

The desired movement of the turntable is described by the rotationaround a fixed axis of rotation. In accordance with FIG. 8, thisrotation can be very simply described as $\begin{matrix}{{\underset{\_}{w}}_{s}^{I} = {{- {\underset{\_}{s}}^{I}} + {{\underset{\underset{\_}{\_}}{T}}_{s}^{PI} \cdot {\underset{\_}{r}}^{P}}}} & (3)\end{matrix}$wherein

-   w _(s) ^(I) Measurable quantity of the desired movement    ${\underset{\underset{\_}{\_}}{T}}_{s}^{PI}$-    Rotation of the desired movement

If here, too, initially only very small rotations are observed, therotation matrix ${\underset{\underset{\_}{\_}}{T}}_{s}^{PI}$results as $\begin{matrix}{{\underset{\underset{\_}{\_}}{T}}_{s}^{PI} = \begin{bmatrix}1 & {- \varphi} & 0 \\\varphi & 1 & 0 \\0 & 0 & 1\end{bmatrix}} & (4)\end{matrix}$

If now the difference between the equations (1) and (3) is formed, thedeviations of the actual movement from the desired movement of theturntable is obtained $\begin{matrix}{{\underset{\_}{\overset{\sim}{w}}}^{I} = {{{\underset{\_}{w}}_{i}^{I} - {\underset{\_}{w}}_{s}^{I}} = {{\underset{\_}{e}}^{I} + {\left( {{\underset{\underset{\_}{\_}}{T}}_{i}^{PI} - {\underset{\underset{\_}{\_}}{T}}_{s}^{PI}} \right) \cdot {\underset{\_}{r}}^{P}}}}} & (5)\end{matrix}$

The associated rotation matrix results as $\begin{matrix}{{\underset{\underset{\_}{\_}}{\overset{\sim}{T}}}^{PI} = {{{\underset{\underset{\_}{\_}}{T}}_{i}^{PI} - {\underset{\underset{\_}{\_}}{T}}_{s}^{PI}} = \begin{bmatrix}0 & {- \delta} & \beta \\\delta & 0 & {- \alpha} \\{- \beta} & \alpha & 0\end{bmatrix}}} & (6)\end{matrix}$

Related to the inertial coordinate system I, the turntable has exactlythree single errors in the sense of the rigid body degrees of freedom

-   Eccentricity e ^(I): Translatory deviations in the direction of the    coordinate system I-   Angle error    ${\underset{\underset{\_}{\_}}{\overset{\sim}{T}}}^{PI}\text{:}$-    Tumble error and orientation error α, β, and δ

These six individual errors can be detected by means of the describedmeasuring arrangement.

Since the entire system is linearized, it is possible to find atransformation rule A, which projects the geometric deviations

 ε=(e _(x) e _(y) e _(x) α β δ)^(T)  (7)

on the measurable quantities{tilde over (w)} =(w _(1z) w _(2y) w _(3z) w _(4y) w _(5z) w_(6y))^(T)  (8)in accordance with equation (5).{tilde over (w)}=A·ε   (9)$\underset{\underset{\_}{\_}}{A} = \begin{bmatrix}0 & 0 & 1 & {{r \cdot S}\quad\psi_{1}} & {{{- r} \cdot C}\quad\psi_{1}} & 0 \\{{- S}\quad\psi_{2}} & {C\quad\psi_{2}} & 0 & 0 & 0 & r \\0 & 0 & 1 & {{r \cdot S}\quad\psi_{3}} & {{{- r} \cdot C}\quad\psi_{3}} & 0 \\{{- S}\quad\psi_{4}} & {C\quad\psi_{4}} & 0 & 0 & 0 & r \\0 & 0 & 1 & {{r \cdot S}\quad\psi_{5}} & {{{- r} \cdot C}\quad\psi_{5}} & 0 \\{{- S}\quad\psi_{6}} & {C\quad\psi_{6}} & 0 & 0 & 0 & r\end{bmatrix}$wherein

-   S{circumflex over (=)}sin and C{circumflex over (=)}cos-   ψ_(i) positional angle of the i-th measuring head (FIG. 5)

The matrix A only contains geometric values resulting from the measuringarrangement. If this matrix A is inverted, the representation of themeasuring errors {tilde over (w)} on the geometric deviation epsilon ofthe measuring arrangement is obtained.ε= A ⁻¹ ·{tilde over (w)}   E(10)wherein ${\underset{\underset{\_}{\_}}{A}}^{- 1} = \begin{bmatrix}0 & \frac{{C\quad\psi_{6}} - {C\quad\psi_{4}}}{K_{1}} & 0 & \frac{{C\quad\psi_{2}} - {C\quad\psi_{6}}}{K_{1}} & 0 & \frac{{C\quad\psi_{4}} - {C\quad\psi_{2}}}{K_{1}} \\0 & \frac{{S\quad\psi_{6}} - {S\quad\psi_{4}}}{K_{1}} & 0 & \frac{{S\quad\psi_{2}} - {S\quad\psi_{6}}}{K_{1}} & 0 & \frac{{S\quad\psi_{4}} - {S\quad\psi_{2}}}{K_{1}} \\{- \frac{S\left( \quad{\psi_{3} - \quad\psi_{5}} \right)}{K_{2}}} & 0 & \frac{S\left( \quad{\psi_{1} - \quad\psi_{5}} \right)}{K_{2}} & 0 & {- \frac{S\left( \quad{\psi_{1} - \quad\psi_{3}} \right)}{K_{2}}} & 0 \\\frac{{C\quad\psi_{5}} - {C\quad\psi_{3}}}{r \cdot K_{2}} & 0 & \frac{{C\quad\psi_{1}} - {C\quad\psi_{5}}}{r \cdot K_{2}} & 0 & \frac{{C\quad\psi_{3}} - {C\quad\psi_{1}}}{r \cdot K_{2}} & 0 \\\frac{{S\quad\psi_{5}} - {S\quad\psi_{3}}}{r \cdot K_{2}} & 0 & \frac{{S\quad\psi_{1}} - {S\quad\psi_{5}}}{r \cdot K_{2}} & 0 & \frac{{S\quad\psi_{3}} - {S\quad\psi_{1}}}{r \cdot K_{2}} & 0 \\0 & \frac{S\left( \quad{\psi_{4} - \quad\psi_{6}} \right)}{r \cdot K_{1}} & 0 & {- \frac{S\left( \quad{\psi_{2} - \quad\psi_{6}} \right)}{r \cdot K_{1}}} & 0 & \frac{S\left( \quad{\psi_{2} - \quad\psi_{4}} \right)}{r \cdot K_{1}}\end{bmatrix}$andK ₁ =S(ψ₂−ψ₄)−S(ψ₂−ψ₆)+S(ψ₄−ψ₆)K ₂ =S(ψ₁−ψ₅)−S(ψ₁−ψ₃)−S(ψ₃−ψ₅)S{circumflex over (=)}sin und C{circumflex over (=)}cos

The equation (10) describes the actual calibration problem, by which itis possible to deduce the geometric deviations of the turntable.

An arrangement of six measuring heads 3, 4, comparable to thearrangement in FIG. 5, for scanning the cylindrical test member 1, whichis provided with a cross grating graduation 13 on its surface 10, isrepresented in FIG. 9, wherein three measuring heads 3 scan the crossgrating graduation 13 (see FIG. 2) in the axial direction, and threefurther measuring heads 4 scan the cross grating graduation 13 in thetangential direction. The measuring heads 3, 4 are arranged in regularangular spacing of 60° along the circumference U of the cylindrical testmember, wherein axially scanning measuring heads 3 and tangentiallyscanning measuring heads 4 are alternatingly arranged. Accordingly, theangles ψ₂ to ψ₆ shown in FIG. 5 have the values of 60°, 120°, 180°, 240°and 300°. A special feature of the exemplary embodiment represented inFIG. 9 lies in the wiring of the measuring heads 3, 4 represented inFIG. 10.

As can be seen by means of FIG. 9, the output signal of each one of themeasuring heads 3, 4 forms a measured value for the measurable quantityw₁, w₂, w₃, w₄, w₅ or w₆, which is to be determined by the respectivemeasuring head 3, 4 by scanning the testing member 1. In accordance withFIG. 10, the measuring heads 3, 4 are wired in such a way that fordetermining the exact angle of rotation of the test member 1 (andtherefore also of the turntable connected therewith), the measuredvalues of the quantities w₂, w₄, w₆ to be measured by the measuringheads 3 scanning the cross grating graduation of the test element 1 areentered with second order terms into the determination of the exactangle of rotation of the test member. In contrast thereto, the measuredvalues of the measurable quantities w₁, w₃, w₅ by the measuring heads 4tangentially scanning the cross grating graduation are entered linearlyinto the corresponding equation. The exact form of the mentionedequation will be derived further down by means of FIG. 11.

It should first be mentioned, however, that by means of the measuringarrangement for the complete determination of the movement state of atest member 1 by means of six measuring heads 3, 4 represented in FIG.9, as well as the wiring of the measuring heads 3, 4 represented in FIG.10, an immediate direct compensation (ONLINE compensation) of theindividual deviations from an ideal rotational movement is possible inorder to determine in this way the exact angle of rotation. In thecourse of this, the individual deviations caused during production,assembly or operation, or eccentricity errors, are taken into account.An essential advantage of the mentioned measuring principle lies in thepossibility of handling the production, assembly and installationtolerances more liberally without affecting the measurement accuracy,i.e. to take less trouble in correcting them. The arrangement describedin accordance with FIGS. 9 and 10 always measures the exact angle ofrotation as a function of a rotating movement of the test member 1, evenin case of substantial eccentricity and run-out errors of the materialmeasure (test element 1 with the cross grating graduation 13 provided onits surface 10). As will be shown in what follows, the only requirementfor this is that the basic mathematical problem can be linearized, i.e.that the occurring individual deviations have a value which permitslinearization without a noticeable loss of accuracy.

As a result, an angular measuring device for a direct measurement of theangle of rotation of turntables is created by means of the arrangementsdescribed in FIGS. 9 and 10, which makes comparatively low demands onthe production and assembly tolerances with respect to the mechanicalparts of the measuring device. The individual deviations of the materialmeasure of the turntable (test member 1 with the assigned cross gratinggraduation), in particular eccentricity and run-out errors of thematerial measure in relation to the stator of the measuring system(measuring heads for scanning the cross grating graduation), can becompletely compensated by means of suitable wiring.

In contrast to the measuring methods, particularly those explained bymeans of FIGS. 4, 5, 7 and 8, it is not intended here for the purpose ofan initial calibration to merely detect an individual deviation in orderto be able to take it into consideration in the course of subsequentmeasurements of the angle of rotation, instead it is possible to performan immediate compensation of the individual deviations in the course ofthe angular measurement (ONLINE compensation).

The equation for determining the angle of rotation of the test member 1,and therefore of the associated rotatable element (for example aturntable) will be derived in what follows by means of FIGS. 9 and 10,together with FIG. 11, in which the actual movement of a test member 1is represented. The derivation is similar to the derivation of thecalibration problem represented by means of FIGS. 7 and 8, by means ofwhich it is possible to make conclusions regarding the geometricdeviations of a turntable. However, a difference consists in that inwhat follows a transformation of the measured value w_(i) into thecoordinate system of the corresponding measuring head (sensor head)takes place.

In accordance with FIG. 11, the description of the general rotation ofthe material measure requires two coordinate systems. Let the coordinatesystem I be the spatially fixed system (stator-fixed system), withrespect to which the movement of the turntable is described. Let thegeometry of the material measure be defined by the coordinate system P.Let the orthogonal transformation TPI, which transforms the coordinatesystem P of the material measure into the coordinate system I, existbetween these two coordinate systems. Then the measurable quantity wj atthe j-th sensor head results from the following equation $\begin{matrix}{w_{j} = {\left\lbrack {{\underset{\underset{\_}{\_}}{T}}^{IS} \cdot \left( {{\underset{\_}{e}}^{I} - {\underset{\_}{s}}_{j}^{I} + {{\underset{\underset{\_}{\_}}{T}}^{PI} \cdot {\underset{\_}{r}}^{P}}} \right)} \right\rbrack^{T} \cdot {\underset{\_}{n}}^{s}}} & \left( 1^{\prime} \right)\end{matrix}$wherein

-   -   e=eccentricity of the material measure e=(e_(x), e_(y),        e_(z))^(T)    -   s=the coordinates of the sensor head (measuring head)    -   r=radius vector of the material measure

T^(PI)=rotation matrix P→I

-   -   T^(IS)=rotation matrix I→S (S coordinate system of the j-th        sensor head)    -   n^(s)=unit vector of the sensor coordinate system in the        measuring direction of the sensor head    -   w_(j)=measurable quantity of the actual movement at the j-th        sensor head (j=1, . . . , 6)

The rotation matrix TPI contains three rotational parameters α, β, andγ=φ+δ, which describes the general rotation of the material measure inrelation to the stator. The vector e characterizes the eccentricity ofthe material measure, as well as its axial movement. A total of sixdeviations results, which can continuously change as a function of theirmanufacture or operation. These six deviations are combined in thevector e=(e_(x), e_(y), e_(z), α, β, δ)^(T). The six measurablequantities wj are also combined in a vector w.

If the Jacobi matrix J is formed for the equation (1′), a relationshipbetween the measurable quantities w and the deviation epsilon resultsw=J·ε   (2′)$\underset{\underset{\_}{\_}}{J} = \begin{bmatrix}\frac{\partial w_{1}}{\partial e_{x}} & \frac{\partial w_{1}}{\partial e_{y}} & \cdots & \frac{\partial w_{1}}{\partial\delta} \\\frac{\partial w_{2}}{\partial e_{x}} & \frac{\partial w_{2}}{\partial e_{y}} & \cdots & \frac{\partial w_{2}}{\partial\delta} \\\vdots & \vdots & ⋰ & \vdots \\\frac{\partial w_{6}}{\partial e_{x}} & \frac{\partial w_{6}}{\partial e_{y}} & \cdots & \frac{\partial w_{6}}{\partial\delta}\end{bmatrix}$wherein

If the Jacobi matrix is linearized by setting

-   sin α≈α, cos α≈1, sin β≈β,-   cos β≈1, sin δ≈δ, cos δ≈1    and the higher order expressions are neglected, the following    results $\underset{\underset{\_}{\_}}{J} = \begin{bmatrix}    {{- \sin}\quad\psi_{1}} & {\cos\quad\psi_{1}} & 0 & {{- r}\quad\sin\quad{\psi_{1}\left( {{\alpha\quad\cos\quad\psi_{1}} - {\beta\quad\sin\quad\psi_{1}}} \right)}} & {r\quad\sin\quad{\psi_{1}\left( {{\beta\quad\cos\quad\psi_{1}} - {\alpha\quad\sin\quad\psi_{1}}} \right)}} & r \\    0 & 0 & 1 & {r\quad\sin\quad\psi_{2}} & {{- r}\quad\cos\quad\psi_{2}} & 0 \\    {{- \sin}\quad\psi_{3}} & {\cos\quad\psi_{3}} & 0 & {{- r}\quad\sin\quad{\psi_{3}\left( {{\alpha\quad\cos\quad\psi_{3}} - {\beta\quad\sin\quad\psi_{3}}} \right)}} & {r\quad\sin\quad{\psi_{3}\left( {{\beta\quad\cos\quad\psi_{3}} - {\alpha\quad\sin\quad\psi_{3}}} \right)}} & r \\    0 & 0 & 1 & {r\quad\sin\quad\psi_{4}} & {{- r}\quad\cos\quad\psi_{4}} & 0 \\    {{- \sin}\quad\psi_{5}} & {\cos\quad\psi_{5}} & 0 & {{- r}\quad\sin\quad{\psi_{5}\left( {{\alpha\quad\cos\quad\psi_{5}} - {\beta\quad\sin\quad\psi_{5}}} \right)}} & {r\quad\sin\quad{\psi_{5}\left( {{\beta\quad\cos\quad\psi_{5}} - {\alpha\quad\sin\quad\psi_{5}}} \right)}} & r \\    0 & 0 & 1 & {r\quad\sin\quad\psi_{6}} & {{- r}\quad\cos\quad\psi_{6}} & 0    \end{bmatrix}$

If now the inverse of the Jacobi matrix is formed, the following isobtained from the equation (2′)ε= J ⁻¹ ·w.  (3′)

Since the Jacobi matrix still contains the variables alpha and beta inlinear form, the equation (3) is explicitly solved for the values e_(x),e_(y), e_(z), α, β, δ and is represented as a function of the sixmeasurable quantities w. In this case the representation of the positionangle error delta as a function of the six measurable quantities w is ofparticular interest. The following is obtainedδ=f(w ₁ , w ₂ , w ₃ , w ₄ , w ₅ , w ₆).  (4′)

It should be noted that the measuring heads which scan the cross gratingdrum in the axial direction by means of the measurable quantities w₂,w₄, w₆ only measure interference movements of the graduation. Incontrast thereto, the desired rotational movement of the graduated drumis superimposed on the interference movement of the measurablequantities w₁, w₃, w₅ by the translatory measuring sensors. It thereforeapplies that the interference movement in the translatory measuringdirection is the difference between the desired movement w_(soll) andthe actual movement ŵ. The following appliesw _(j) =w _(soll) −ŵ _(j) =r·φ−ŵ _(j) (j=1, 3, 5)  (5′)

With the equation (5′), the following follows from equation (4′):δ=f(w ₁ , rφ−ŵ ₂ , w ₃ , rφ−ŵ ₄ , w ₅ , rφ−ŵ ₆)¹=0.  (6′)

If in equation (6′) the position angle error δ is made zero, and theequation is solved for the desired angle φ, the desired angle φ followsas a function of the six measurable quantities w.φ=k ₁ w ₁ +k ₂ w ₂ ² +k ₃ w ₃ +k ₄ w ₄ ² +k ₅ w ₅ +k ₆ w ₆ ² +k ₇ w ₂ w⁴ +k ₈ w ₂ w ₆ +k ₉ w ₄ w ₆  (7′)

The constant factors k₁ result from the geometric arrangement of thesensors and the graduation radius r. They must be calculated for eachcase of use (symbolically possible, but very complicated expressions).

The correction equation (7′) makes an ONLINE correction of the angularmeasurement possible. Measuring errors inevitably occur in the course ofthe angular measurement because of production and assembly tolerances.If the six interference movements are directly measured by the use ofsix measuring heads, the effects of first order and second order angularerrors can be compensated by a skillful wiring of the six individualmeasurable quantities (FIG. 10). The correction equation provides thewiring diagram, including parameterization, for the six measuring pointsin the respective geometric measuring arrangement.

While the correction equation is mathematically unequivocal, theparameters k_(i) (i=1, 2, 3, 4, 5, 6, 7, 8, 9, ) in equation (7′) aresubject to some uncertainties. These uncertainties are caused in thatthe relative arrangement of the measuring heads, essentially these arethe angles ψ_(j) of the measuring heads and the graduation radius r(FIG. 9), must be exactly known in order to achieve an exactdetermination of the angle of rotation φ. In actuality the values ψ_(j)and r will also be subject to production-caused variations. It istherefore recommended to identify the constant factors k₁ for a sensorarrangement in accordance with FIG. 9 by means of a system measurementdevice. The advantage lies in that graduation errors of the graduateddisk, production and assembly errors of the seating of the graduateddisk, as well as uncertainties regarding the sensor arrangement arecompletely taken into account in the equation (7′).

Eccentricity errors in the angular measurement have the effect ofso-called 1-φ errors. But tumble errors lead to 2-φ errors. It isunimportant for the correction method whether the eccentricity error(1-φ error) is a result of assembly, production or installation errors,or is the result of a long-wave graduation error. It is also unimportantwhether the tumble error (2-φ error) is the result of assembly,production or installation errors, or is the result of a long-wavegraduation error.

In summation, the measuring arrangement described by means of FIGS. 9 to11 offers the following advantages:

complete compensation of the measuring errors by means of suitablewiring of the six individual measurable quantities,

for angular measuring systems with their own bearing: high measurementaccuracy along with the reduction of production and assembly tolerancesfor the mechanical components (lowering of costs),

for angular measuring systems without their own bearing: simplifiedassembly because of reduced requirements made on the running toleranceof the installation parts,

increase of thermal stability, since thermally-related eccentricity andrun-out errors are compensated.

Parameterization of the circuits can take place, on the one hand, bydetecting the factors k₁ by calculation (see the example described inwhat follows). Or the parameter factors k₁) are obtained by anidentification by means of measuring technology on a system measuringdevice. Here, the advantage lies in the complete taking into account ofgraduation errors in the graduated disk, production and assembly errorsof the graduated disk seating, as well as uncertainties in the sensorarrangement.

The employment of additional measuring heads (past the six measuringheads represented in FIG. 9) furthermore makes the compensation ofhigher order eccentricity of axial wobble errors possible, for example,respectively four scanning operations in a 90° arrangement tangentiallyand axially (a total of eight scanning points).

In what follows, an application of the above described methods inconnection with an angle measuring system of the type described by meansof FIGS. 9 to 11 with cross grating graduation and six measuring heads.

Assumed are:

-   -   radius of the test member 1:r=125 mm,    -   material measure: cross grating graduation on the cylinder        surface of the test member,    -   measurement arrangement: six cross grating measuring heads at        distances of respectively 60°, i.e. ψ₁=0°, ψ₂=60° etc. (see FIG.        9).

In this case, the following results for the Jacobi matrix$\underset{\underset{\_}{\_}}{J} = \begin{bmatrix}0 & 1 & 0 & 0 & 0 & 125 \\0 & 0 & 1 & 108.2532 & {- 62.5} & 0 \\{- 0.866} & {- 0.5} & 0 & {{54.1266\quad\alpha} + {93.75\quad\beta}} & {{{- 54.1266}\quad\beta} - {93.75\quad\alpha}} & 125 \\0 & 0 & 1 & 0 & 125 & 0 \\0.866 & {- 0.5} & 0 & {{{- 54.1266}\quad\alpha} + {93.75\quad\beta}} & {{54.1266\quad\beta} - {93.75\quad\alpha}} & 125 \\0 & 0 & 1 & {- 108.2532} & {- 62.5} & 0\end{bmatrix}$

If the Jacobi matrix is inverted, and the equation (3) is resolved withrespect to the unknown ε=(e₁, e₂, e₃, α, β, δ)^(T), the following isobtained for delta: $\begin{matrix}{\gamma = {{{0.267 \cdot 10^{- 2}}w_{1}} - {{0.169 \cdot 10^{- 14}}w_{2}^{2}} + {{0.267 \cdot 10^{- 2}}w_{3}} - \ldots +}} \\{{{0.912 \cdot 10^{- 17}}w_{4}^{2}} + {{0.267 \cdot 10^{- 2}}w_{5}} + {{0.133 \cdot 10^{- 14}}w_{6}^{2}} + \ldots +} \\{{{0.799 \cdot 10^{- 14}}w_{2}w_{4}} - {{0.498 \cdot 10^{- 14}}w_{2}w_{6}} - {{0.246 \cdot 10^{- 14}}w_{4}w_{6}}}\end{matrix}$

Using the equation (5′), finally the corrected (actual) angle ofrotation φ in accordance with equation (7′) results from the equation(6′).

For an eccentricity of 0.1 mm, the method produces a 1-φ residual errorof approximately 2.8·10-8 seconds of arc, and with an additional wobbleerror of 0.62 mm at the graduation circumference, a dominant 2-φresidual error of approximately 1.2 seconds of arc results.

The invention may be embodied in other forms than those secificallydisclosed herein without departing from its spirit or essentialcharateristics. The described embodiments are to be considered in allrespects only as illustrative and not restrictive, and the scope of theinvention is commensurate with th appended claims rather than theforegoing description.

1. A device for detecting the rotational movement of an element which isrotatably arranged around an axis, the device comprising: a materialmeasure that rotates about axis of rotation; a first measuringgraduation provided on said material measure and which scans along afirst direction, which has a component along said axis of rotation; asecond measuring graduation provided on said material measure, whereinboth said first measuring graduation and said second measuringgraduation surround said axis of rotation in a ring shape, and which canhe scanned along said first direction and a second direction that islinearly independent of said first direction; and at least threemeasuring heads, which are spaced apart from each other along acircumferential direction which surrounds said axis of rotation, areassigned to each of said first measuring graduation and said secondmeasuring graduation for scanning said first measuring graduation andsaid second measuring graduations.
 2. The device in accordance withclaim 1, wherein said first measuring graduation and said secondmeasuring graduation are each formed by line graduations.
 3. The devicein accordance with claim 1, wherein said first measuring graduation andsaid second measuring graduation are scanned vertically with respect toeach other.
 4. The device in accordance with claim 2, wherein said linegraduations of said first measuring graduation extend vertically withrespect to said line graduations of said second measuring graduation. 5.The device in accordance with claim 2, wherein said line graduations ofsaid first measuring graduation extend parallel with said axis ofrotation.
 6. The device in accordance with claim 2, wherein said linegraduations of said first measuring graduation extend perpendicularlywith respect to said axis of rotation.
 7. The device in accordance withclaim 1, wherein said first measuring graduation is scanned in saidfirst direction, and said second measuring graduation is scanned in saidsecond direction.
 8. The device in accordance with claim 1, wherein saidfirst measuring graduation and said second measuring graduation are eachformed by corresponding incremental measuring graduations.
 9. The devicein accordance with claim 1, wherein said first measuring graduation andsaid second measuring graduation are each formed by a correspondingcross grating graduation.
 10. The device in accordance with claim 9,wherein each of said cross grating graduations extends on a surface ofsaid material measure along the circumference of said material measure.11. The device in accordance with claim 1, wherein said first measuringgraduation and said second measuring graduation are spatially separatedfrom each other.
 12. The device in accordance with claim 11, whereinsaid first measuring graduation is arranged on a surface of saidmaterial measure, and said second measuring graduation is arranged on acircumferential surface of said material measure, which projects outwardfrom said surface of said material measure.
 13. The device in accordancewith claim 11, wherein six measured values are generated by said threemeasuring heads, which represent six independent individual deviationsfrom said axis of rotation.
 14. The device in accordance with claim 1,wherein a resulting measuring direction of said first direction and saidsecond direction at each measuring point measured by said at least threemeasuring heads is respectively located on a straight line, which isoriented skewed with respect to said axis of rotation.
 15. The device inaccordance with claim 1, further comprising a reference track providedat said material measure.
 16. The device in accordance with claim 1,wherein said material measure comprises a cylindrical surface.
 17. Thedevice in accordance with claim 1, wherein each of sand three measuringheads is embodied as a cross grating measuring head.
 18. The device inaccordance with claim 1, comprising three additional measuring heads forscanning said first measuring graduation and said second measuringgraduation, wherein said three measuring heads scan said first measuringgraduation and said three additional measuring heads scan said secondmeasuring graduation.
 19. The device in accordance with claim 18,wherein said three measuring heads and said additional three measuringheads are arranged alternatingly behind each other.
 20. The device inaccordance with claim 1, wherein said material measure is arrangedcoaxially about an element that rotates about said axis of rotation; andsaid three measuring heads are wired in such a way with respect to eachother that an angle of rotation of said element is determined frommeasured values generated by said three measuring heads.
 21. The devicein accordance with claim 18, wherein said material measure is arrangedcoaxially about an element that rotates about said axis of rotation; andsaid three measuring heads and said three additional measuring heads arewired in such a way with respect to each other that first measurablequantities from said three measuring heads provided for scanning saidfirst measuring graduation are linked together for forming second orderterms in said first measurable quantities, and that second measurablequantities from said three additional measuring heads provided forscanning said second measuring graduation are linearly entered relatedwith an angle of rotation of said clement which has to be determined.22. The device in accordance with claim 21, wherein said firstmeasurable quantities are linked together for forming second order termsin said first measurable quantities, and that said second measurablequantities are linearly entered into the determination of said angle ofrotation of said element.
 23. The device in accordance with claim 1,further comprising an additional measuring head for generating aredundant output signal.
 24. The device in accordance with claim 1,wherein each of said three are arranged at constant angular distancesbehind each other.
 25. The device in accordance with claim 1, whereinsaid three measuring heads are arranged on a common support.
 26. Thedevice in accordance with claim 25, wherein thermal expansion behaviorof said common support is essentially identical with thermal expansionbehavior of a support of said first measuring graduation and said secondmeasuring graduation.
 27. A method for detecting rotational movement ofan element which rotates around axis of rotation, the method comprising:arranging a first measuring graduation that surrounds an axis ofrotation around which an element rotates; arranging a second measuringgraduation at surrounds said axis of rotation; scanning said firstmeasuring graduation along a first direction having a component alongsaid axis of rotation, wherein said scanning said first measuringgraduation takes place in at least three locations, which are spacedapart from each other in a circumferential direction surrounding saidaxis of rotation, and scanning said second measuring graduating along asecond direction that is linearly independent of said first direction,wherein said scanning said second measuring graduation takes place in atleast three locations, which are spaced apart from each other in saidcircumferential direction surrounding said axis of rotation.
 28. Themethod in accordance with claim 27, further comprising determiningindividual deviations of said element.
 29. The method in accordance withclaim 27, further comprising compensating individual deviations of saidelement.
 30. The method in accordance with claim 27, wherein said firstdirection extends perpendicularly with respect to said second direction.31. The method in accordance with claim 30, wherein said scanning saidfirst measuring graduation is performed along a direction parallel withsaid axis of rotation, and said scanning said second measuringgraduation in performed in a tangential direction with respect to saidaxis of rotation.
 32. The method in accordance with claim 27, whereinsaid first measuring graduation and said second measuring graduationeach comprise an incremental measuring graduation.
 33. The method inaccordance with claim 27, wherein said scanning said first measuringgraduation and said scanning said second measuring graduation results inthe generation of six output signals as measurable quantities thatrepresent six independent individual deviations of said axis ofrotation.
 34. The method in accordance with claim 27, wherein aresulting measuring direction of said first measuring direction and saidsecond measuring direction at each of said at least three locations isrespectively located on a straight line, which is oriented skewed withrespect to said axis of rotation.
 35. The method in accordance withclaim 27, wherein said scanning said first measuring graduationcomprises moving a measuring head relative to said first measuringgraduation by at least one revolution.